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On some discontinuous fixed point mappings in convex metric spaces. (English) Zbl 0814.47065
This article deals with nonlinear operators \(T\) in metric linear spaces satisfying either the condition \[ d(Tx, Ty)\leq ad(x, y)+ (1- a)\max \{d(x, Tx), d(y, Ty), b[d(x, Ty)+ d(y, Tx)]\} \] with \(0\leq a< 1\) and \(b\leq {1\over 2}- (1- a^ 2)/(10+ 6a^ 2)\) or the condition \[ d(Tx, Ty)\leq ad(x, y)+ b[d(x, Ty)+ d(y, Tx)]+ c\max \{d(x, Tx), d(y, Ty)\} \] with \(0\leq a< 1\), \(b\), \(c\geq 0\), \(a+ b> 0\) and \(a+ b(5+ a^ 2)/(2+ a^ 2)+ c\leq 1\). The main results are the fixed point theorems for such operators.
Reviewer: P.Zabreiko (Minsk)

47H10 Fixed-point theorems
Full Text: EuDML
[1] Lj. B. Ćirič: Generalized contractions and fixed-point theorems. Publ. Inst. Math. (Beograd) 26 (1971), 19-26. · Zbl 0234.54029
[2] Lj. B. Ćirič: On a common fixed point theorem of a Greguš type. Publ. Inst. Math. (Beograd) 63 (1991), no. 49, 174-178. · Zbl 0753.54023
[3] D. Delbosco, O. Ferrero and F. Rossati: Teoremi di punto fisso per applicazioni negli spazi di Banach. Boll. Un. Math. Ital. 2-A (1983), no. 6, 297-303. · Zbl 0532.47046
[4] M. L. Diviccaro, B. Fisher and S. Sessa: A common fixed point theorem of Greguš type. Publ. Math. Debrecen 34 (1987), no. 1-2, 83-89. · Zbl 0634.47051
[5] B. Fisher: Common fixed points on a Banach space. Chung Yuan J. 11 (1982), 19-26.
[6] B. Fisher and S. Sessa: On a fixed point theorem of Greguš. Internat. J. Math. Math. Sci. 9 (1986), no. 1, 23-28. · Zbl 0597.47036 · doi:10.1155/S0161171286000030 · eudml:46091
[7] M. Greguš: A fixed point theorem in Banach space. Boll. Un. Mat. Ital. 5 (1980), no. 17-A, 193-198. · Zbl 0538.47035
[8] B. Y. Li: Fixed point theorems of nonexpansive mappings in convex metric spaces. Appl. Math. Mech. (English Ed) 10 (1989), no. 2, 183-188. · Zbl 0752.47022 · doi:10.1007/BF02014826
[9] R. N. Mukherjee and V. Verma: A note on a fixed point theorem of Greguš. Math. Japon 33 (1988), 745-749. · Zbl 0655.47047
[10] W. Takahashi: A convexity in metric space and nonexpansive mappings I. Kodai Math. Sem. Rep. 22 (1970), 142-149. · Zbl 0268.54048 · doi:10.2996/kmj/1138846111
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